1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
|
/*
** libproj -- library of cartographic projections
**
** Copyright (c) 2005, 2006 Gerald I. Evenden
*/
static const char
LIBPROJ_ID[] = "Id";
/*
** Permission is hereby granted, free of charge, to any person obtaining
** a copy of this software and associated documentation files (the
** "Software"), to deal in the Software without restriction, including
** without limitation the rights to use, copy, modify, merge, publish,
** distribute, sublicense, and/or sell copies of the Software, and to
** permit persons to whom the Software is furnished to do so, subject to
** the following conditions:
**
** The above copyright notice and this permission notice shall be
** included in all copies or substantial portions of the Software.
**
** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
** EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
** MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
** IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
** CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
** TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
** SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
#define GUYOU 1
#define PEIRCE_Q 2
#define ADAMS_HEMI 3
#define ADAMS_WSI 4
#define ADAMS_WSII 5
#define TOL 1e-9
#define RSQRT2 0.7071067811865475244008443620
#define PROJ_LIB__
#define PROJ_PARMS__ \
int mode;
#include <lib_proj.h>
PROJ_HEAD(guyou, "Guyou") "\n\tMisc., Sph., NoInv.";
PROJ_HEAD(peirce_q, "Pierce Quincuncial") "\n\tMisc., Sph., NoInv.";
PROJ_HEAD(adams_hemi, "Adams Hemisphere in a Square") "\n\tMisc., Sph., NoInv.";
PROJ_HEAD(adams_wsI, "Adams World in a Square I") "\n\tMisc., Sph., NoInv.";
PROJ_HEAD(adams_wsII, "Adams World in a Square II") "\n\tMisc., Sph., NoInv.";
#define TWO_OVER_PI 0.6366197723675813430755350534
#define ORDER 8
/* Procedure to compute elliptic integral of the first kind
* where k^2=0.5. Precision good to better than 1e-7
* The approximation is performed with an even Chebyshev
* series, thus the coefficients below are the even values
* and where series evaluation must be multiplied by the argument. */
double
ell_int_5(double phi) {
int i = ORDER;
double d1 = 0., d2 = 0., y, y2, temp;
const double C[] = { /* even coefficients */
2.19174570831038,
0.0914203033408211,
-0.00575574836830288,
-0.0012804644680613,
5.30394739921063e-05,
3.12960480765314e-05,
2.02692115653689e-07,
-8.58691003636495e-07};
double const *Cp = C + ORDER - 1;
y = phi * TWO_OVER_PI;
y = 2. * y * y - 1.;
y2 = 2. * y;
while (--i) {
temp = d1;
d1 = y2 * d1 - d2 + *Cp--;
d2 = temp;
}
return phi * (y * d1 - d2 + 0.5 * *Cp);
}
FORWARD(s_forward); /* spheroid */
double m, n, a=0., b=0.;
int sm=0, sn=0;
switch (P->mode) {
case GUYOU:
if ((fabs(lp.lam) - TOL) > HALFPI) F_ERROR;
if (fabs(fabs(lp.phi) - HALFPI) < TOL) {
xy.x = 0;
xy.y = lp.phi < 0 ? -1.85407 : 1.85407;
return xy;
} else {
double sl = sin(lp.lam);
double sp = sin(lp.phi);
double cp = cos(lp.phi);
a = proj_acos((cp * sl - sp) * RSQRT2);
b = proj_acos((cp * sl + sp) * RSQRT2);
sm = lp.lam < 0.;
sn = lp.phi < 0.;
}
break;
case PEIRCE_Q: {
double sl = sin(lp.lam);
double cl = cos(lp.lam);
double cp = cos(lp.phi);
a = proj_acos(cp * (sl + cl) * RSQRT2);
b = proj_acos(cp * (sl - cl) * RSQRT2);
sm = sl < 0.;
sn = cl > 0.;
}
break;
case ADAMS_HEMI: {
double sp = sin(lp.phi);
if ((fabs(lp.lam) - TOL) > HALFPI) F_ERROR;
a = cos(lp.phi) * sin(lp.lam);
sm = (sp + a) < 0.;
sn = (sp - a) < 0.;
a = proj_acos(a);
b = HALFPI - lp.phi;
}
break;
case ADAMS_WSI: {
double sp = tan(0.5 * lp.phi);
b = cos(proj_asin(sp)) * sin(0.5 * lp.lam);
a = proj_acos((b - sp) * RSQRT2);
b = proj_acos((b + sp) * RSQRT2);
sm = lp.lam < 0.;
sn = lp.phi < 0.;
}
break;
case ADAMS_WSII: {
double spp = tan(0.5 * lp.phi);
a = cos(proj_asin(spp)) * sin(0.5 * lp.lam);
sm = (spp + a) < 0.;
sn = (spp - a) < 0.;
b = proj_acos(spp);
a = proj_acos(a);
}
break;
}
m = proj_asin(sqrt(fabs(1. + cos(a + b))));
if (sm) m = -m;
n = proj_asin(sqrt(fabs(1. - cos(a - b))));
if (sn) n = -n;
xy.x = ell_int_5(m);
xy.y = ell_int_5(n);
if (P->mode == ADAMS_HEMI || P->mode == ADAMS_WSII) { /* rotate by 45deg. */
double temp = xy.x;
xy.x = RSQRT2 * (xy.x - xy.y);
xy.y = RSQRT2 * (temp + xy.y);
}
return (xy);
}
FREEUP; if (P) free(P); }
static void*
setup(PROJ *P) {
P->es = 0;
P->fwd = s_forward;
return P;
}
ENTRY0(guyou) P->mode = GUYOU; ENDENTRY(setup(P))
ENTRY0(peirce_q) P->mode = PEIRCE_Q; ENDENTRY(setup(P))
ENTRY0(adams_hemi) P->mode = ADAMS_HEMI; ENDENTRY(setup(P))
ENTRY0(adams_wsI) P->mode = ADAMS_WSI; ENDENTRY(setup(P))
ENTRY0(adams_wsII) P->mode = ADAMS_WSII; ENDENTRY(setup(P))
/*
** Log: proj_guyou.c
** Revision 3.2 2008/06/26 14:48:50 gie
** initialized some parameters
**
** Revision 3.1 2006/01/11 01:38:18 gie
** Initial
**
*/
|
